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Diffstat (limited to 'lib/python2.7/test/decimaltestdata/multiply.decTest')
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diff --git a/lib/python2.7/test/decimaltestdata/multiply.decTest b/lib/python2.7/test/decimaltestdata/multiply.decTest new file mode 100644 index 0000000..6a23d5a --- /dev/null +++ b/lib/python2.7/test/decimaltestdata/multiply.decTest @@ -0,0 +1,731 @@ +------------------------------------------------------------------------ +-- multiply.decTest -- decimal multiplication -- +-- Copyright (c) IBM Corporation, 1981, 2008. All rights reserved. -- +------------------------------------------------------------------------ +-- Please see the document "General Decimal Arithmetic Testcases" -- +-- at http://www2.hursley.ibm.com/decimal for the description of -- +-- these testcases. -- +-- -- +-- These testcases are experimental ('beta' versions), and they -- +-- may contain errors. They are offered on an as-is basis. In -- +-- particular, achieving the same results as the tests here is not -- +-- a guarantee that an implementation complies with any Standard -- +-- or specification. The tests are not exhaustive. -- +-- -- +-- Please send comments, suggestions, and corrections to the author: -- +-- Mike Cowlishaw, IBM Fellow -- +-- IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK -- +-- mfc@uk.ibm.com -- +------------------------------------------------------------------------ +version: 2.59 + +extended: 1 +precision: 9 +rounding: half_up +maxExponent: 384 +minexponent: -383 + +-- sanity checks (as base, above) +mulx000 multiply 2 2 -> 4 +mulx001 multiply 2 3 -> 6 +mulx002 multiply 5 1 -> 5 +mulx003 multiply 5 2 -> 10 +mulx004 multiply 1.20 2 -> 2.40 +mulx005 multiply 1.20 0 -> 0.00 +mulx006 multiply 1.20 -2 -> -2.40 +mulx007 multiply -1.20 2 -> -2.40 +mulx008 multiply -1.20 0 -> -0.00 +mulx009 multiply -1.20 -2 -> 2.40 +mulx010 multiply 5.09 7.1 -> 36.139 +mulx011 multiply 2.5 4 -> 10.0 +mulx012 multiply 2.50 4 -> 10.00 +mulx013 multiply 1.23456789 1.00000000 -> 1.23456789 Rounded +mulx014 multiply 9.999999999 9.999999999 -> 100.000000 Inexact Rounded +mulx015 multiply 2.50 4 -> 10.00 +precision: 6 +mulx016 multiply 2.50 4 -> 10.00 +mulx017 multiply 9.999999999 9.999999999 -> 100.000 Inexact Rounded +mulx018 multiply 9.999999999 -9.999999999 -> -100.000 Inexact Rounded +mulx019 multiply -9.999999999 9.999999999 -> -100.000 Inexact Rounded +mulx020 multiply -9.999999999 -9.999999999 -> 100.000 Inexact Rounded + +-- 1999.12.21: next one is a edge case if intermediate longs are used +precision: 15 +mulx059 multiply 999999999999 9765625 -> 9.76562499999023E+18 Inexact Rounded +precision: 30 +mulx160 multiply 999999999999 9765625 -> 9765624999990234375 +precision: 9 +----- + +-- zeros, etc. +mulx021 multiply 0 0 -> 0 +mulx022 multiply 0 -0 -> -0 +mulx023 multiply -0 0 -> -0 +mulx024 multiply -0 -0 -> 0 +mulx025 multiply -0.0 -0.0 -> 0.00 +mulx026 multiply -0.0 -0.0 -> 0.00 +mulx027 multiply -0.0 -0.0 -> 0.00 +mulx028 multiply -0.0 -0.0 -> 0.00 +mulx030 multiply 5.00 1E-3 -> 0.00500 +mulx031 multiply 00.00 0.000 -> 0.00000 +mulx032 multiply 00.00 0E-3 -> 0.00000 -- rhs is 0 +mulx033 multiply 0E-3 00.00 -> 0.00000 -- lhs is 0 +mulx034 multiply -5.00 1E-3 -> -0.00500 +mulx035 multiply -00.00 0.000 -> -0.00000 +mulx036 multiply -00.00 0E-3 -> -0.00000 -- rhs is 0 +mulx037 multiply -0E-3 00.00 -> -0.00000 -- lhs is 0 +mulx038 multiply 5.00 -1E-3 -> -0.00500 +mulx039 multiply 00.00 -0.000 -> -0.00000 +mulx040 multiply 00.00 -0E-3 -> -0.00000 -- rhs is 0 +mulx041 multiply 0E-3 -00.00 -> -0.00000 -- lhs is 0 +mulx042 multiply -5.00 -1E-3 -> 0.00500 +mulx043 multiply -00.00 -0.000 -> 0.00000 +mulx044 multiply -00.00 -0E-3 -> 0.00000 -- rhs is 0 +mulx045 multiply -0E-3 -00.00 -> 0.00000 -- lhs is 0 + +-- examples from decarith +mulx050 multiply 1.20 3 -> 3.60 +mulx051 multiply 7 3 -> 21 +mulx052 multiply 0.9 0.8 -> 0.72 +mulx053 multiply 0.9 -0 -> -0.0 +mulx054 multiply 654321 654321 -> 4.28135971E+11 Inexact Rounded + +mulx060 multiply 123.45 1e7 -> 1.2345E+9 +mulx061 multiply 123.45 1e8 -> 1.2345E+10 +mulx062 multiply 123.45 1e+9 -> 1.2345E+11 +mulx063 multiply 123.45 1e10 -> 1.2345E+12 +mulx064 multiply 123.45 1e11 -> 1.2345E+13 +mulx065 multiply 123.45 1e12 -> 1.2345E+14 +mulx066 multiply 123.45 1e13 -> 1.2345E+15 + + +-- test some intermediate lengths +precision: 9 +mulx080 multiply 0.1 123456789 -> 12345678.9 +mulx081 multiply 0.1 1234567891 -> 123456789 Inexact Rounded +mulx082 multiply 0.1 12345678912 -> 1.23456789E+9 Inexact Rounded +mulx083 multiply 0.1 12345678912345 -> 1.23456789E+12 Inexact Rounded +mulx084 multiply 0.1 123456789 -> 12345678.9 +precision: 8 +mulx085 multiply 0.1 12345678912 -> 1.2345679E+9 Inexact Rounded +mulx086 multiply 0.1 12345678912345 -> 1.2345679E+12 Inexact Rounded +precision: 7 +mulx087 multiply 0.1 12345678912 -> 1.234568E+9 Inexact Rounded +mulx088 multiply 0.1 12345678912345 -> 1.234568E+12 Inexact Rounded + +precision: 9 +mulx090 multiply 123456789 0.1 -> 12345678.9 +mulx091 multiply 1234567891 0.1 -> 123456789 Inexact Rounded +mulx092 multiply 12345678912 0.1 -> 1.23456789E+9 Inexact Rounded +mulx093 multiply 12345678912345 0.1 -> 1.23456789E+12 Inexact Rounded +mulx094 multiply 123456789 0.1 -> 12345678.9 +precision: 8 +mulx095 multiply 12345678912 0.1 -> 1.2345679E+9 Inexact Rounded +mulx096 multiply 12345678912345 0.1 -> 1.2345679E+12 Inexact Rounded +precision: 7 +mulx097 multiply 12345678912 0.1 -> 1.234568E+9 Inexact Rounded +mulx098 multiply 12345678912345 0.1 -> 1.234568E+12 Inexact Rounded + +-- test some more edge cases and carries +maxexponent: 9999 +minexponent: -9999 +precision: 33 +mulx101 multiply 9 9 -> 81 +mulx102 multiply 9 90 -> 810 +mulx103 multiply 9 900 -> 8100 +mulx104 multiply 9 9000 -> 81000 +mulx105 multiply 9 90000 -> 810000 +mulx106 multiply 9 900000 -> 8100000 +mulx107 multiply 9 9000000 -> 81000000 +mulx108 multiply 9 90000000 -> 810000000 +mulx109 multiply 9 900000000 -> 8100000000 +mulx110 multiply 9 9000000000 -> 81000000000 +mulx111 multiply 9 90000000000 -> 810000000000 +mulx112 multiply 9 900000000000 -> 8100000000000 +mulx113 multiply 9 9000000000000 -> 81000000000000 +mulx114 multiply 9 90000000000000 -> 810000000000000 +mulx115 multiply 9 900000000000000 -> 8100000000000000 +mulx116 multiply 9 9000000000000000 -> 81000000000000000 +mulx117 multiply 9 90000000000000000 -> 810000000000000000 +mulx118 multiply 9 900000000000000000 -> 8100000000000000000 +mulx119 multiply 9 9000000000000000000 -> 81000000000000000000 +mulx120 multiply 9 90000000000000000000 -> 810000000000000000000 +mulx121 multiply 9 900000000000000000000 -> 8100000000000000000000 +mulx122 multiply 9 9000000000000000000000 -> 81000000000000000000000 +mulx123 multiply 9 90000000000000000000000 -> 810000000000000000000000 +-- test some more edge cases without carries +mulx131 multiply 3 3 -> 9 +mulx132 multiply 3 30 -> 90 +mulx133 multiply 3 300 -> 900 +mulx134 multiply 3 3000 -> 9000 +mulx135 multiply 3 30000 -> 90000 +mulx136 multiply 3 300000 -> 900000 +mulx137 multiply 3 3000000 -> 9000000 +mulx138 multiply 3 30000000 -> 90000000 +mulx139 multiply 3 300000000 -> 900000000 +mulx140 multiply 3 3000000000 -> 9000000000 +mulx141 multiply 3 30000000000 -> 90000000000 +mulx142 multiply 3 300000000000 -> 900000000000 +mulx143 multiply 3 3000000000000 -> 9000000000000 +mulx144 multiply 3 30000000000000 -> 90000000000000 +mulx145 multiply 3 300000000000000 -> 900000000000000 +mulx146 multiply 3 3000000000000000 -> 9000000000000000 +mulx147 multiply 3 30000000000000000 -> 90000000000000000 +mulx148 multiply 3 300000000000000000 -> 900000000000000000 +mulx149 multiply 3 3000000000000000000 -> 9000000000000000000 +mulx150 multiply 3 30000000000000000000 -> 90000000000000000000 +mulx151 multiply 3 300000000000000000000 -> 900000000000000000000 +mulx152 multiply 3 3000000000000000000000 -> 9000000000000000000000 +mulx153 multiply 3 30000000000000000000000 -> 90000000000000000000000 + +maxexponent: 999999999 +minexponent: -999999999 +precision: 9 +-- test some cases that are close to exponent overflow/underflow +mulx170 multiply 1 9e999999999 -> 9E+999999999 +mulx171 multiply 1 9.9e999999999 -> 9.9E+999999999 +mulx172 multiply 1 9.99e999999999 -> 9.99E+999999999 +mulx173 multiply 9e999999999 1 -> 9E+999999999 +mulx174 multiply 9.9e999999999 1 -> 9.9E+999999999 +mulx176 multiply 9.99e999999999 1 -> 9.99E+999999999 +mulx177 multiply 1 9.99999999e999999999 -> 9.99999999E+999999999 +mulx178 multiply 9.99999999e999999999 1 -> 9.99999999E+999999999 + +mulx180 multiply 0.1 9e-999999998 -> 9E-999999999 +mulx181 multiply 0.1 99e-999999998 -> 9.9E-999999998 +mulx182 multiply 0.1 999e-999999998 -> 9.99E-999999997 + +mulx183 multiply 0.1 9e-999999998 -> 9E-999999999 +mulx184 multiply 0.1 99e-999999998 -> 9.9E-999999998 +mulx185 multiply 0.1 999e-999999998 -> 9.99E-999999997 +mulx186 multiply 0.1 999e-999999997 -> 9.99E-999999996 +mulx187 multiply 0.1 9999e-999999997 -> 9.999E-999999995 +mulx188 multiply 0.1 99999e-999999997 -> 9.9999E-999999994 + +mulx190 multiply 1 9e-999999998 -> 9E-999999998 +mulx191 multiply 1 99e-999999998 -> 9.9E-999999997 +mulx192 multiply 1 999e-999999998 -> 9.99E-999999996 +mulx193 multiply 9e-999999998 1 -> 9E-999999998 +mulx194 multiply 99e-999999998 1 -> 9.9E-999999997 +mulx195 multiply 999e-999999998 1 -> 9.99E-999999996 + +mulx196 multiply 1e-599999999 1e-400000000 -> 1E-999999999 +mulx197 multiply 1e-600000000 1e-399999999 -> 1E-999999999 +mulx198 multiply 1.2e-599999999 1.2e-400000000 -> 1.44E-999999999 +mulx199 multiply 1.2e-600000000 1.2e-399999999 -> 1.44E-999999999 + +mulx201 multiply 1e599999999 1e400000000 -> 1E+999999999 +mulx202 multiply 1e600000000 1e399999999 -> 1E+999999999 +mulx203 multiply 1.2e599999999 1.2e400000000 -> 1.44E+999999999 +mulx204 multiply 1.2e600000000 1.2e399999999 -> 1.44E+999999999 + +-- long operand triangle +precision: 33 +mulx246 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193369671916511992830 Inexact Rounded +precision: 32 +mulx247 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119336967191651199283 Inexact Rounded +precision: 31 +mulx248 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011933696719165119928 Inexact Rounded +precision: 30 +mulx249 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193369671916511993 Inexact Rounded +precision: 29 +mulx250 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119336967191651199 Inexact Rounded +precision: 28 +mulx251 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011933696719165120 Inexact Rounded +precision: 27 +mulx252 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193369671916512 Inexact Rounded +precision: 26 +mulx253 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119336967191651 Inexact Rounded +precision: 25 +mulx254 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011933696719165 Inexact Rounded +precision: 24 +mulx255 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193369671917 Inexact Rounded +precision: 23 +mulx256 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119336967192 Inexact Rounded +precision: 22 +mulx257 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011933696719 Inexact Rounded +precision: 21 +mulx258 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193369672 Inexact Rounded +precision: 20 +mulx259 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119336967 Inexact Rounded +precision: 19 +mulx260 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011933697 Inexact Rounded +precision: 18 +mulx261 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193370 Inexact Rounded +precision: 17 +mulx262 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119337 Inexact Rounded +precision: 16 +mulx263 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908011934 Inexact Rounded +precision: 15 +mulx264 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801193 Inexact Rounded +precision: 14 +mulx265 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080119 Inexact Rounded +precision: 13 +mulx266 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908012 Inexact Rounded +precision: 12 +mulx267 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.290801 Inexact Rounded +precision: 11 +mulx268 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29080 Inexact Rounded +precision: 10 +mulx269 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.2908 Inexact Rounded +precision: 9 +mulx270 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.291 Inexact Rounded +precision: 8 +mulx271 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.29 Inexact Rounded +precision: 7 +mulx272 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433.3 Inexact Rounded +precision: 6 +mulx273 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 145433 Inexact Rounded +precision: 5 +mulx274 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 1.4543E+5 Inexact Rounded +precision: 4 +mulx275 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 1.454E+5 Inexact Rounded +precision: 3 +mulx276 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 1.45E+5 Inexact Rounded +precision: 2 +mulx277 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 1.5E+5 Inexact Rounded +precision: 1 +mulx278 multiply 30269.587755640502150977251770554 4.8046009735990873395936309640543 -> 1E+5 Inexact Rounded + +-- test some edge cases with exact rounding +maxexponent: 9999 +minexponent: -9999 +precision: 9 +mulx301 multiply 9 9 -> 81 +mulx302 multiply 9 90 -> 810 +mulx303 multiply 9 900 -> 8100 +mulx304 multiply 9 9000 -> 81000 +mulx305 multiply 9 90000 -> 810000 +mulx306 multiply 9 900000 -> 8100000 +mulx307 multiply 9 9000000 -> 81000000 +mulx308 multiply 9 90000000 -> 810000000 +mulx309 multiply 9 900000000 -> 8.10000000E+9 Rounded +mulx310 multiply 9 9000000000 -> 8.10000000E+10 Rounded +mulx311 multiply 9 90000000000 -> 8.10000000E+11 Rounded +mulx312 multiply 9 900000000000 -> 8.10000000E+12 Rounded +mulx313 multiply 9 9000000000000 -> 8.10000000E+13 Rounded +mulx314 multiply 9 90000000000000 -> 8.10000000E+14 Rounded +mulx315 multiply 9 900000000000000 -> 8.10000000E+15 Rounded +mulx316 multiply 9 9000000000000000 -> 8.10000000E+16 Rounded +mulx317 multiply 9 90000000000000000 -> 8.10000000E+17 Rounded +mulx318 multiply 9 900000000000000000 -> 8.10000000E+18 Rounded +mulx319 multiply 9 9000000000000000000 -> 8.10000000E+19 Rounded +mulx320 multiply 9 90000000000000000000 -> 8.10000000E+20 Rounded +mulx321 multiply 9 900000000000000000000 -> 8.10000000E+21 Rounded +mulx322 multiply 9 9000000000000000000000 -> 8.10000000E+22 Rounded +mulx323 multiply 9 90000000000000000000000 -> 8.10000000E+23 Rounded + +-- fastpath breakers +precision: 29 +mulx330 multiply 1.491824697641270317824852952837224 1.105170918075647624811707826490246514675628614562883537345747603 -> 1.6487212707001281468486507878 Inexact Rounded +precision: 55 +mulx331 multiply 0.8958341352965282506768545828765117803873717284891040428 0.8958341352965282506768545828765117803873717284891040428 -> 0.8025187979624784829842553829934069955890983696752228299 Inexact Rounded + + +-- tryzeros cases +precision: 7 +rounding: half_up +maxExponent: 92 +minexponent: -92 +mulx504 multiply 0E-60 1000E-60 -> 0E-98 Clamped +mulx505 multiply 100E+60 0E+60 -> 0E+92 Clamped + +-- mixed with zeros +maxexponent: 999999999 +minexponent: -999999999 +precision: 9 +mulx541 multiply 0 -1 -> -0 +mulx542 multiply -0 -1 -> 0 +mulx543 multiply 0 1 -> 0 +mulx544 multiply -0 1 -> -0 +mulx545 multiply -1 0 -> -0 +mulx546 multiply -1 -0 -> 0 +mulx547 multiply 1 0 -> 0 +mulx548 multiply 1 -0 -> -0 + +mulx551 multiply 0.0 -1 -> -0.0 +mulx552 multiply -0.0 -1 -> 0.0 +mulx553 multiply 0.0 1 -> 0.0 +mulx554 multiply -0.0 1 -> -0.0 +mulx555 multiply -1.0 0 -> -0.0 +mulx556 multiply -1.0 -0 -> 0.0 +mulx557 multiply 1.0 0 -> 0.0 +mulx558 multiply 1.0 -0 -> -0.0 + +mulx561 multiply 0 -1.0 -> -0.0 +mulx562 multiply -0 -1.0 -> 0.0 +mulx563 multiply 0 1.0 -> 0.0 +mulx564 multiply -0 1.0 -> -0.0 +mulx565 multiply -1 0.0 -> -0.0 +mulx566 multiply -1 -0.0 -> 0.0 +mulx567 multiply 1 0.0 -> 0.0 +mulx568 multiply 1 -0.0 -> -0.0 + +mulx571 multiply 0.0 -1.0 -> -0.00 +mulx572 multiply -0.0 -1.0 -> 0.00 +mulx573 multiply 0.0 1.0 -> 0.00 +mulx574 multiply -0.0 1.0 -> -0.00 +mulx575 multiply -1.0 0.0 -> -0.00 +mulx576 multiply -1.0 -0.0 -> 0.00 +mulx577 multiply 1.0 0.0 -> 0.00 +mulx578 multiply 1.0 -0.0 -> -0.00 + + +-- Specials +mulx580 multiply Inf -Inf -> -Infinity +mulx581 multiply Inf -1000 -> -Infinity +mulx582 multiply Inf -1 -> -Infinity +mulx583 multiply Inf -0 -> NaN Invalid_operation +mulx584 multiply Inf 0 -> NaN Invalid_operation +mulx585 multiply Inf 1 -> Infinity +mulx586 multiply Inf 1000 -> Infinity +mulx587 multiply Inf Inf -> Infinity +mulx588 multiply -1000 Inf -> -Infinity +mulx589 multiply -Inf Inf -> -Infinity +mulx590 multiply -1 Inf -> -Infinity +mulx591 multiply -0 Inf -> NaN Invalid_operation +mulx592 multiply 0 Inf -> NaN Invalid_operation +mulx593 multiply 1 Inf -> Infinity +mulx594 multiply 1000 Inf -> Infinity +mulx595 multiply Inf Inf -> Infinity + +mulx600 multiply -Inf -Inf -> Infinity +mulx601 multiply -Inf -1000 -> Infinity +mulx602 multiply -Inf -1 -> Infinity +mulx603 multiply -Inf -0 -> NaN Invalid_operation +mulx604 multiply -Inf 0 -> NaN Invalid_operation +mulx605 multiply -Inf 1 -> -Infinity +mulx606 multiply -Inf 1000 -> -Infinity +mulx607 multiply -Inf Inf -> -Infinity +mulx608 multiply -1000 Inf -> -Infinity +mulx609 multiply -Inf -Inf -> Infinity +mulx610 multiply -1 -Inf -> Infinity +mulx611 multiply -0 -Inf -> NaN Invalid_operation +mulx612 multiply 0 -Inf -> NaN Invalid_operation +mulx613 multiply 1 -Inf -> -Infinity +mulx614 multiply 1000 -Inf -> -Infinity +mulx615 multiply Inf -Inf -> -Infinity + +mulx621 multiply NaN -Inf -> NaN +mulx622 multiply NaN -1000 -> NaN +mulx623 multiply NaN -1 -> NaN +mulx624 multiply NaN -0 -> NaN +mulx625 multiply NaN 0 -> NaN +mulx626 multiply NaN 1 -> NaN +mulx627 multiply NaN 1000 -> NaN +mulx628 multiply NaN Inf -> NaN +mulx629 multiply NaN NaN -> NaN +mulx630 multiply -Inf NaN -> NaN +mulx631 multiply -1000 NaN -> NaN +mulx632 multiply -1 NaN -> NaN +mulx633 multiply -0 NaN -> NaN +mulx634 multiply 0 NaN -> NaN +mulx635 multiply 1 NaN -> NaN +mulx636 multiply 1000 NaN -> NaN +mulx637 multiply Inf NaN -> NaN + +mulx641 multiply sNaN -Inf -> NaN Invalid_operation +mulx642 multiply sNaN -1000 -> NaN Invalid_operation +mulx643 multiply sNaN -1 -> NaN Invalid_operation +mulx644 multiply sNaN -0 -> NaN Invalid_operation +mulx645 multiply sNaN 0 -> NaN Invalid_operation +mulx646 multiply sNaN 1 -> NaN Invalid_operation +mulx647 multiply sNaN 1000 -> NaN Invalid_operation +mulx648 multiply sNaN NaN -> NaN Invalid_operation +mulx649 multiply sNaN sNaN -> NaN Invalid_operation +mulx650 multiply NaN sNaN -> NaN Invalid_operation +mulx651 multiply -Inf sNaN -> NaN Invalid_operation +mulx652 multiply -1000 sNaN -> NaN Invalid_operation +mulx653 multiply -1 sNaN -> NaN Invalid_operation +mulx654 multiply -0 sNaN -> NaN Invalid_operation +mulx655 multiply 0 sNaN -> NaN Invalid_operation +mulx656 multiply 1 sNaN -> NaN Invalid_operation +mulx657 multiply 1000 sNaN -> NaN Invalid_operation +mulx658 multiply Inf sNaN -> NaN Invalid_operation +mulx659 multiply NaN sNaN -> NaN Invalid_operation + +-- propagating NaNs +mulx661 multiply NaN9 -Inf -> NaN9 +mulx662 multiply NaN8 999 -> NaN8 +mulx663 multiply NaN71 Inf -> NaN71 +mulx664 multiply NaN6 NaN5 -> NaN6 +mulx665 multiply -Inf NaN4 -> NaN4 +mulx666 multiply -999 NaN33 -> NaN33 +mulx667 multiply Inf NaN2 -> NaN2 + +mulx671 multiply sNaN99 -Inf -> NaN99 Invalid_operation +mulx672 multiply sNaN98 -11 -> NaN98 Invalid_operation +mulx673 multiply sNaN97 NaN -> NaN97 Invalid_operation +mulx674 multiply sNaN16 sNaN94 -> NaN16 Invalid_operation +mulx675 multiply NaN95 sNaN93 -> NaN93 Invalid_operation +mulx676 multiply -Inf sNaN92 -> NaN92 Invalid_operation +mulx677 multiply 088 sNaN91 -> NaN91 Invalid_operation +mulx678 multiply Inf sNaN90 -> NaN90 Invalid_operation +mulx679 multiply NaN sNaN89 -> NaN89 Invalid_operation + +mulx681 multiply -NaN9 -Inf -> -NaN9 +mulx682 multiply -NaN8 999 -> -NaN8 +mulx683 multiply -NaN71 Inf -> -NaN71 +mulx684 multiply -NaN6 -NaN5 -> -NaN6 +mulx685 multiply -Inf -NaN4 -> -NaN4 +mulx686 multiply -999 -NaN33 -> -NaN33 +mulx687 multiply Inf -NaN2 -> -NaN2 + +mulx691 multiply -sNaN99 -Inf -> -NaN99 Invalid_operation +mulx692 multiply -sNaN98 -11 -> -NaN98 Invalid_operation +mulx693 multiply -sNaN97 NaN -> -NaN97 Invalid_operation +mulx694 multiply -sNaN16 -sNaN94 -> -NaN16 Invalid_operation +mulx695 multiply -NaN95 -sNaN93 -> -NaN93 Invalid_operation +mulx696 multiply -Inf -sNaN92 -> -NaN92 Invalid_operation +mulx697 multiply 088 -sNaN91 -> -NaN91 Invalid_operation +mulx698 multiply Inf -sNaN90 -> -NaN90 Invalid_operation +mulx699 multiply -NaN -sNaN89 -> -NaN89 Invalid_operation + +mulx701 multiply -NaN -Inf -> -NaN +mulx702 multiply -NaN 999 -> -NaN +mulx703 multiply -NaN Inf -> -NaN +mulx704 multiply -NaN -NaN -> -NaN +mulx705 multiply -Inf -NaN0 -> -NaN +mulx706 multiply -999 -NaN -> -NaN +mulx707 multiply Inf -NaN -> -NaN + +mulx711 multiply -sNaN -Inf -> -NaN Invalid_operation +mulx712 multiply -sNaN -11 -> -NaN Invalid_operation +mulx713 multiply -sNaN00 NaN -> -NaN Invalid_operation +mulx714 multiply -sNaN -sNaN -> -NaN Invalid_operation +mulx715 multiply -NaN -sNaN -> -NaN Invalid_operation +mulx716 multiply -Inf -sNaN -> -NaN Invalid_operation +mulx717 multiply 088 -sNaN -> -NaN Invalid_operation +mulx718 multiply Inf -sNaN -> -NaN Invalid_operation +mulx719 multiply -NaN -sNaN -> -NaN Invalid_operation + +-- overflow and underflow tests .. note subnormal results +maxexponent: 999999999 +minexponent: -999999999 +mulx730 multiply +1.23456789012345E-0 9E+999999999 -> Infinity Inexact Overflow Rounded +mulx731 multiply 9E+999999999 +1.23456789012345E-0 -> Infinity Inexact Overflow Rounded +mulx732 multiply +0.100 9E-999999999 -> 9.00E-1000000000 Subnormal +mulx733 multiply 9E-999999999 +0.100 -> 9.00E-1000000000 Subnormal +mulx735 multiply -1.23456789012345E-0 9E+999999999 -> -Infinity Inexact Overflow Rounded +mulx736 multiply 9E+999999999 -1.23456789012345E-0 -> -Infinity Inexact Overflow Rounded +mulx737 multiply -0.100 9E-999999999 -> -9.00E-1000000000 Subnormal +mulx738 multiply 9E-999999999 -0.100 -> -9.00E-1000000000 Subnormal + +mulx739 multiply 1e-599999999 1e-400000001 -> 1E-1000000000 Subnormal +mulx740 multiply 1e-599999999 1e-400000000 -> 1E-999999999 +mulx741 multiply 1e-600000000 1e-400000000 -> 1E-1000000000 Subnormal +mulx742 multiply 9e-999999998 0.01 -> 9E-1000000000 Subnormal +mulx743 multiply 9e-999999998 0.1 -> 9E-999999999 +mulx744 multiply 0.01 9e-999999998 -> 9E-1000000000 Subnormal +mulx745 multiply 1e599999999 1e400000001 -> Infinity Overflow Inexact Rounded +mulx746 multiply 1e599999999 1e400000000 -> 1E+999999999 +mulx747 multiply 1e600000000 1e400000000 -> Infinity Overflow Inexact Rounded +mulx748 multiply 9e999999998 100 -> Infinity Overflow Inexact Rounded +mulx749 multiply 9e999999998 10 -> 9.0E+999999999 +mulx750 multiply 100 9e999999998 -> Infinity Overflow Inexact Rounded +-- signs +mulx751 multiply 1e+777777777 1e+411111111 -> Infinity Overflow Inexact Rounded +mulx752 multiply 1e+777777777 -1e+411111111 -> -Infinity Overflow Inexact Rounded +mulx753 multiply -1e+777777777 1e+411111111 -> -Infinity Overflow Inexact Rounded +mulx754 multiply -1e+777777777 -1e+411111111 -> Infinity Overflow Inexact Rounded +mulx755 multiply 1e-777777777 1e-411111111 -> 0E-1000000007 Underflow Subnormal Inexact Rounded Clamped +mulx756 multiply 1e-777777777 -1e-411111111 -> -0E-1000000007 Underflow Subnormal Inexact Rounded Clamped +mulx757 multiply -1e-777777777 1e-411111111 -> -0E-1000000007 Underflow Subnormal Inexact Rounded Clamped +mulx758 multiply -1e-777777777 -1e-411111111 -> 0E-1000000007 Underflow Subnormal Inexact Rounded Clamped + +-- 'subnormal' boundary (all hard underflow or overflow in base arithemtic) +precision: 9 +mulx760 multiply 1e-600000000 1e-400000001 -> 1E-1000000001 Subnormal +mulx761 multiply 1e-600000000 1e-400000002 -> 1E-1000000002 Subnormal +mulx762 multiply 1e-600000000 1e-400000003 -> 1E-1000000003 Subnormal +mulx763 multiply 1e-600000000 1e-400000004 -> 1E-1000000004 Subnormal +mulx764 multiply 1e-600000000 1e-400000005 -> 1E-1000000005 Subnormal +mulx765 multiply 1e-600000000 1e-400000006 -> 1E-1000000006 Subnormal +mulx766 multiply 1e-600000000 1e-400000007 -> 1E-1000000007 Subnormal +mulx767 multiply 1e-600000000 1e-400000008 -> 0E-1000000007 Underflow Subnormal Inexact Rounded Clamped +mulx768 multiply 1e-600000000 1e-400000009 -> 0E-1000000007 Underflow Subnormal Inexact Rounded Clamped +mulx769 multiply 1e-600000000 1e-400000010 -> 0E-1000000007 Underflow Subnormal Inexact Rounded Clamped +-- [no equivalent of 'subnormal' for overflow] +mulx770 multiply 1e+600000000 1e+400000001 -> Infinity Overflow Inexact Rounded +mulx771 multiply 1e+600000000 1e+400000002 -> Infinity Overflow Inexact Rounded +mulx772 multiply 1e+600000000 1e+400000003 -> Infinity Overflow Inexact Rounded +mulx773 multiply 1e+600000000 1e+400000004 -> Infinity Overflow Inexact Rounded +mulx774 multiply 1e+600000000 1e+400000005 -> Infinity Overflow Inexact Rounded +mulx775 multiply 1e+600000000 1e+400000006 -> Infinity Overflow Inexact Rounded +mulx776 multiply 1e+600000000 1e+400000007 -> Infinity Overflow Inexact Rounded +mulx777 multiply 1e+600000000 1e+400000008 -> Infinity Overflow Inexact Rounded +mulx778 multiply 1e+600000000 1e+400000009 -> Infinity Overflow Inexact Rounded +mulx779 multiply 1e+600000000 1e+400000010 -> Infinity Overflow Inexact Rounded + +-- 'subnormal' test edge condition at higher precisions +precision: 99 +mulx780 multiply 1e-600000000 1e-400000007 -> 1E-1000000007 Subnormal +mulx781 multiply 1e-600000000 1e-400000008 -> 1E-1000000008 Subnormal +mulx782 multiply 1e-600000000 1e-400000097 -> 1E-1000000097 Subnormal +mulx783 multiply 1e-600000000 1e-400000098 -> 0E-1000000097 Underflow Subnormal Inexact Rounded Clamped +precision: 999 +mulx784 multiply 1e-600000000 1e-400000997 -> 1E-1000000997 Subnormal +mulx785 multiply 1e-600000000 1e-400000998 -> 0E-1000000997 Underflow Subnormal Inexact Rounded Clamped + +-- following testcases [through mulx800] not yet run against code +precision: 9999 +mulx786 multiply 1e-600000000 1e-400009997 -> 1E-1000009997 Subnormal +mulx787 multiply 1e-600000000 1e-400009998 -> 0E-1000009997 Underflow Subnormal Inexact Rounded Clamped +precision: 99999 +mulx788 multiply 1e-600000000 1e-400099997 -> 1E-1000099997 Subnormal +mulx789 multiply 1e-600000000 1e-400099998 -> 0E-1000099997 Underflow Subnormal Inexact Rounded Clamped +precision: 999999 +mulx790 multiply 1e-600000000 1e-400999997 -> 1E-1000999997 Subnormal +mulx791 multiply 1e-600000000 1e-400999998 -> 0E-1000999997 Underflow Subnormal Inexact Rounded Clamped +precision: 9999999 +mulx792 multiply 1e-600000000 1e-409999997 -> 1E-1009999997 Subnormal +mulx793 multiply 1e-600000000 1e-409999998 -> 0E-1009999997 Underflow Subnormal Inexact Rounded Clamped +precision: 99999999 +mulx794 multiply 1e-600000000 1e-499999997 -> 1E-1099999997 Subnormal +mulx795 multiply 1e-600000000 1e-499999998 -> 0E-1099999997 Underflow Subnormal Inexact Rounded Clamped +precision: 999999999 +mulx796 multiply 1e-999999999 1e-999999997 -> 1E-1999999996 Subnormal +mulx797 multiply 1e-999999999 1e-999999998 -> 1E-1999999997 Subnormal +mulx798 multiply 1e-999999999 1e-999999999 -> 0E-1999999997 Underflow Subnormal Inexact Rounded Clamped +mulx799 multiply 1e-600000000 1e-400000007 -> 1E-1000000007 Subnormal +mulx800 multiply 1e-600000000 1e-400000008 -> 1E-1000000008 Subnormal + +-- test subnormals rounding +precision: 5 +maxExponent: 999 +minexponent: -999 +rounding: half_even + +mulx801 multiply 1.0000E-999 1 -> 1.0000E-999 +mulx802 multiply 1.000E-999 1e-1 -> 1.000E-1000 Subnormal +mulx803 multiply 1.00E-999 1e-2 -> 1.00E-1001 Subnormal +mulx804 multiply 1.0E-999 1e-3 -> 1.0E-1002 Subnormal +mulx805 multiply 1.0E-999 1e-4 -> 1E-1003 Subnormal Rounded +mulx806 multiply 1.3E-999 1e-4 -> 1E-1003 Underflow Subnormal Inexact Rounded +mulx807 multiply 1.5E-999 1e-4 -> 2E-1003 Underflow Subnormal Inexact Rounded +mulx808 multiply 1.7E-999 1e-4 -> 2E-1003 Underflow Subnormal Inexact Rounded +mulx809 multiply 2.3E-999 1e-4 -> 2E-1003 Underflow Subnormal Inexact Rounded +mulx810 multiply 2.5E-999 1e-4 -> 2E-1003 Underflow Subnormal Inexact Rounded +mulx811 multiply 2.7E-999 1e-4 -> 3E-1003 Underflow Subnormal Inexact Rounded +mulx812 multiply 1.49E-999 1e-4 -> 1E-1003 Underflow Subnormal Inexact Rounded +mulx813 multiply 1.50E-999 1e-4 -> 2E-1003 Underflow Subnormal Inexact Rounded +mulx814 multiply 1.51E-999 1e-4 -> 2E-1003 Underflow Subnormal Inexact Rounded +mulx815 multiply 2.49E-999 1e-4 -> 2E-1003 Underflow Subnormal Inexact Rounded +mulx816 multiply 2.50E-999 1e-4 -> 2E-1003 Underflow Subnormal Inexact Rounded +mulx817 multiply 2.51E-999 1e-4 -> 3E-1003 Underflow Subnormal Inexact Rounded + +mulx818 multiply 1E-999 1e-4 -> 1E-1003 Subnormal +mulx819 multiply 3E-999 1e-5 -> 0E-1003 Underflow Subnormal Inexact Rounded Clamped +mulx820 multiply 5E-999 1e-5 -> 0E-1003 Underflow Subnormal Inexact Rounded Clamped +mulx821 multiply 7E-999 1e-5 -> 1E-1003 Underflow Subnormal Inexact Rounded +mulx822 multiply 9E-999 1e-5 -> 1E-1003 Underflow Subnormal Inexact Rounded +mulx823 multiply 9.9E-999 1e-5 -> 1E-1003 Underflow Subnormal Inexact Rounded + +mulx824 multiply 1E-999 -1e-4 -> -1E-1003 Subnormal +mulx825 multiply 3E-999 -1e-5 -> -0E-1003 Underflow Subnormal Inexact Rounded Clamped +mulx826 multiply -5E-999 1e-5 -> -0E-1003 Underflow Subnormal Inexact Rounded Clamped +mulx827 multiply 7E-999 -1e-5 -> -1E-1003 Underflow Subnormal Inexact Rounded +mulx828 multiply -9E-999 1e-5 -> -1E-1003 Underflow Subnormal Inexact Rounded +mulx829 multiply 9.9E-999 -1e-5 -> -1E-1003 Underflow Subnormal Inexact Rounded +mulx830 multiply 3.0E-999 -1e-5 -> -0E-1003 Underflow Subnormal Inexact Rounded Clamped + +mulx831 multiply 1.0E-501 1e-501 -> 1.0E-1002 Subnormal +mulx832 multiply 2.0E-501 2e-501 -> 4.0E-1002 Subnormal +mulx833 multiply 4.0E-501 4e-501 -> 1.60E-1001 Subnormal +mulx834 multiply 10.0E-501 10e-501 -> 1.000E-1000 Subnormal +mulx835 multiply 30.0E-501 30e-501 -> 9.000E-1000 Subnormal +mulx836 multiply 40.0E-501 40e-501 -> 1.6000E-999 + +-- squares +mulx840 multiply 1E-502 1e-502 -> 0E-1003 Underflow Subnormal Inexact Rounded Clamped +mulx841 multiply 1E-501 1e-501 -> 1E-1002 Subnormal +mulx842 multiply 2E-501 2e-501 -> 4E-1002 Subnormal +mulx843 multiply 4E-501 4e-501 -> 1.6E-1001 Subnormal +mulx844 multiply 10E-501 10e-501 -> 1.00E-1000 Subnormal +mulx845 multiply 30E-501 30e-501 -> 9.00E-1000 Subnormal +mulx846 multiply 40E-501 40e-501 -> 1.600E-999 + +-- cubes +mulx850 multiply 1E-670 1e-335 -> 0E-1003 Underflow Subnormal Inexact Rounded Clamped +mulx851 multiply 1E-668 1e-334 -> 1E-1002 Subnormal +mulx852 multiply 4E-668 2e-334 -> 8E-1002 Subnormal +mulx853 multiply 9E-668 3e-334 -> 2.7E-1001 Subnormal +mulx854 multiply 16E-668 4e-334 -> 6.4E-1001 Subnormal +mulx855 multiply 25E-668 5e-334 -> 1.25E-1000 Subnormal +mulx856 multiply 10E-668 100e-334 -> 1.000E-999 + +-- test derived from result of 0.099 ** 999 at 15 digits with unlimited exponent +precision: 19 +mulx860 multiply 6636851557994578716E-520 6636851557994578716E-520 -> 4.40477986028551E-1003 Underflow Subnormal Inexact Rounded + +-- Long operand overflow may be a different path +precision: 3 +maxExponent: 999999999 +minexponent: -999999999 +mulx870 multiply 1 9.999E+999999999 -> Infinity Inexact Overflow Rounded +mulx871 multiply 1 -9.999E+999999999 -> -Infinity Inexact Overflow Rounded +mulx872 multiply 9.999E+999999999 1 -> Infinity Inexact Overflow Rounded +mulx873 multiply -9.999E+999999999 1 -> -Infinity Inexact Overflow Rounded + +-- check for double-rounded subnormals +precision: 5 +maxexponent: 79 +minexponent: -79 +mulx881 multiply 1.2347E-40 1.2347E-40 -> 1.524E-80 Inexact Rounded Subnormal Underflow +mulx882 multiply 1.234E-40 1.234E-40 -> 1.523E-80 Inexact Rounded Subnormal Underflow +mulx883 multiply 1.23E-40 1.23E-40 -> 1.513E-80 Inexact Rounded Subnormal Underflow +mulx884 multiply 1.2E-40 1.2E-40 -> 1.44E-80 Subnormal +mulx885 multiply 1.2E-40 1.2E-41 -> 1.44E-81 Subnormal +mulx886 multiply 1.2E-40 1.2E-42 -> 1.4E-82 Subnormal Inexact Rounded Underflow +mulx887 multiply 1.2E-40 1.3E-42 -> 1.6E-82 Subnormal Inexact Rounded Underflow +mulx888 multiply 1.3E-40 1.3E-42 -> 1.7E-82 Subnormal Inexact Rounded Underflow +mulx889 multiply 1.3E-40 1.3E-43 -> 2E-83 Subnormal Inexact Rounded Underflow +mulx890 multiply 1.3E-41 1.3E-43 -> 0E-83 Clamped Subnormal Inexact Rounded Underflow + +mulx891 multiply 1.2345E-39 1.234E-40 -> 1.5234E-79 Inexact Rounded +mulx892 multiply 1.23456E-39 1.234E-40 -> 1.5234E-79 Inexact Rounded +mulx893 multiply 1.2345E-40 1.234E-40 -> 1.523E-80 Inexact Rounded Subnormal Underflow +mulx894 multiply 1.23456E-40 1.234E-40 -> 1.523E-80 Inexact Rounded Subnormal Underflow +mulx895 multiply 1.2345E-41 1.234E-40 -> 1.52E-81 Inexact Rounded Subnormal Underflow +mulx896 multiply 1.23456E-41 1.234E-40 -> 1.52E-81 Inexact Rounded Subnormal Underflow + +-- Now explore the case where we get a normal result with Underflow +precision: 16 +rounding: half_up +maxExponent: 384 +minExponent: -383 + +mulx900 multiply 0.3000000000E-191 0.3000000000E-191 -> 9.00000000000000E-384 Subnormal Rounded +mulx901 multiply 0.3000000001E-191 0.3000000001E-191 -> 9.00000000600000E-384 Underflow Inexact Subnormal Rounded +mulx902 multiply 9.999999999999999E-383 0.0999999999999 -> 9.99999999999000E-384 Underflow Inexact Subnormal Rounded +mulx903 multiply 9.999999999999999E-383 0.09999999999999 -> 9.99999999999900E-384 Underflow Inexact Subnormal Rounded +mulx904 multiply 9.999999999999999E-383 0.099999999999999 -> 9.99999999999990E-384 Underflow Inexact Subnormal Rounded +mulx905 multiply 9.999999999999999E-383 0.0999999999999999 -> 9.99999999999999E-384 Underflow Inexact Subnormal Rounded +-- prove operands are exact +mulx906 multiply 9.999999999999999E-383 1 -> 9.999999999999999E-383 +mulx907 multiply 1 0.09999999999999999 -> 0.09999999999999999 +-- the next rounds to Nmin +mulx908 multiply 9.999999999999999E-383 0.09999999999999999 -> 1.000000000000000E-383 Underflow Inexact Subnormal Rounded +mulx909 multiply 9.999999999999999E-383 0.099999999999999999 -> 1.000000000000000E-383 Underflow Inexact Subnormal Rounded +mulx910 multiply 9.999999999999999E-383 0.0999999999999999999 -> 1.000000000000000E-383 Underflow Inexact Subnormal Rounded +mulx911 multiply 9.999999999999999E-383 0.09999999999999999999 -> 1.000000000000000E-383 Underflow Inexact Subnormal Rounded + + +-- Examples from SQL proposal (Krishna Kulkarni) +precision: 34 +rounding: half_up +maxExponent: 6144 +minExponent: -6143 +mulx1001 multiply 130E-2 120E-2 -> 1.5600 +mulx1002 multiply 130E-2 12E-1 -> 1.560 +mulx1003 multiply 130E-2 1E0 -> 1.30 +mulx1004 multiply 1E2 1E4 -> 1E+6 + +-- payload decapitate +precision: 5 +mulx1010 multiply 11 -sNaN1234567890 -> -NaN67890 Invalid_operation + +-- Null tests +mulx990 multiply 10 # -> NaN Invalid_operation +mulx991 multiply # 10 -> NaN Invalid_operation + |